Struggling with the question
A and B are the points (2, 4) and (0, 7). P is a point on the line AB:
(b) Find the value of for which is parallel to 2i − 2j
I have written the point OP as the vector $(2-2\lambda)\textbf{i} + (4+3\lambda)\textbf{j}$ but I'm not sure where to go from there.
To make $\color{blue}{(2-2\lambda)}\textbf{i} + \color{blue}{(4+3\lambda)}\textbf{j}$ parallel to $\color{green}2\mathbf i-\color{green}2\mathbf j$,
set $\color{blue}{2-2\lambda}=\color{green}2\kappa$ and $\color{blue}{4+3\lambda}=\color{green}{-2}\kappa$.
Add both equations and solve for $\lambda.$